Constant force and constant velocity experiments in concentrated suspensions

摘要

Homogeneous materials are characterized by intrinsic properties such as density, thermal conductivity, and viscosity that are independent of sample size and of the state of stress of the material. For example, experiments with a test sphere traversing in a homogeneous Newtonian fluid would determine the same viscosity by measuring the force on the test sphere traveling at a constant velocity or by measuring the velocity of the test sphere under a constant force. Einstein (1906) showed that for monodisperse suspensions under bulk flow conditions at infinite dilution the viscosity was a material property.;Theoretical calculations show that a test sphere settling in suspensions of neutrally buoyant spheres will experience a larger resistance to motion traveling at a constant velocity through a region in the cylinder free of end effects than moving under a constant force when the spheres are of similar size or the test sphere is much smaller than the suspending spheres. Hence, constant force and constant velocity experiments would measure different apparent viscosities even in a suspension at infinite dilution. This appears to be a contradiction of Einstein's result. The objective of this paper is to examine this surprising prediction using concentrated suspensions of neutrally buoyant particles in viscous Newtonian liquids under conditions such that only hydrodynamic forces exert an appreciable effect.;Experiments have been performed to explore the difference between the apparent viscosity of a suspension as determined by a constant gravitational force applied to a test sphere (falling-ball rheometry) and the apparent viscosity of the same suspension measured with a non-rotating test sphere towed (pulling-ball rheometry) with uniform velocity through the suspension. The relative viscosity in both the falling-ball and pulling-ball experiments were determined by normalizing the suspension results to the pure fluid results. This reduced viscosity was found to be significantly larger for the pulling-ball than that found from the falling-ball, and this effect increases linearly as the volume fraction of solids in the suspension, &phis;, increases from 0.1 to 0.5. These experimental results are in qualitative agreement with the theoretical predictions made by Almog and Brenner (1997) for infinitely dilute suspensions.